Quantum searching, counting and amplitude amplification by eigenvector analysis

Grovers quantum searching algorithm uses a quantum computer to find the solution to fx for a given function f The algorithm which repeatedly applies a certain operator G has led to a major family of quantum algorithms for generating and counting solutions to fx for more general f By studying the eigenvectors and eigenvalues of G and its variations we arrive at simple algorithms and analyses for quantum searching approximate counting and amplitude amplication and estimatio